Method for solving deformation of cross-water bridge based on beidou-3 / gnss inversion

Abstract

This invention discloses a method for calculating the deformation of a cross-water bridge based on BeiDou-3 / GNSS inversion, specifically relating to the field of bridge monitoring technology. The steps are as follows: Based on the satellites observable by the bridge structure monitoring station, an observation equation is established by combining all satellites; the observation equation is solved using the matrix method to obtain the predicted state vector and the covariance matrix of the state vector of the bridge structure deformation; considering the influence of gross errors in BeiDou-3 / GNSS observations, an adaptive factor is proposed to correct the predicted value of the state vector; the vector K and the updated state vector covariance are obtained; considering that there are still gross errors in the BeiDou-3 / GNSS carrier phase observations, a robust factor M is introduced to determine the weight of each type of observation; the K matrix and the state covariance matrix are updated using the corrected measurement covariance matrix R; the updated state vector is calculated. This invention solves the problem of low accuracy in conventional BeiDou / GNSS data processing methods, improving the accuracy of bridge deformation calculation.

Description

Technical Field

[0001] This invention relates to the field of bridge monitoring technology, and in particular to a method for solving the deformation of cross-water bridges based on BeiDou-3 / GNSS inversion. Background Technology

[0002] In Bridge Structure Health Monitoring (BSHM), deformation response is a crucial indicator of structural safety. Deformation reflects the structural performance degradation and damage under load. Accurately capturing bridge structural deformation allows for timely monitoring of the bridge's dynamic response and health status under load, ensuring its service life, improving structural resilience, and providing valuable insights for managers in formulating bridge maintenance policies.

[0003] Traditional methods for monitoring bridge structural deformation involve using measuring instruments such as total stations and levels. While these methods offer high accuracy, they also suffer from high labor intensity, low efficiency, and high costs. BeiDou-3 / GNSS technology, on the other hand, enables real-time, all-weather, and automated measurements, significantly reducing labor intensity and improving efficiency. It has broad application prospects in bridge construction control, intelligent construction, and information-based maintenance.

[0004] like Figure 1 As shown, the current conventional method for processing BeiDou-3 / GNSS data is to first calculate the coordinate sequence of the bridge structure monitoring station, and then obtain the deformation value through differential coordinates. This method suffers from problems such as error accumulation and the introduction of absolute coordinate errors. Furthermore, based on the principle of resection of distances between BeiDou-3 / GNSS satellites and bridge structure monitoring stations, it does not consider the inherent characteristics of bridge structure deformation, which limits the accuracy of BeiDou-3 / GNSS in sensing transient bridge deformation. Summary of the Invention

[0005] The present invention aims to provide a method for solving the deformation of cross-water bridges based on BeiDou-3 / GNSS inversion, which solves the problem of low accuracy in conventional BeiDou / GNSS data processing methods.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows: a method for solving the deformation of cross-water bridges based on BeiDou-3 / GNSS inversion, comprising the following steps:

[0007] S1. Based on the satellites that can be observed by the bridge structure monitoring station, establish the observation equation from the Beidou-3 / GNSS monitoring station to the satellite carrier phase observation value by combining all satellites;

[0008] S2. Solve the observation equations using the matrix method to obtain the predicted state vector of the bridge structure deformation and the covariance matrix of the state vector considering different satellite observation accuracies.

[0009] S3. Considering the impact of gross errors in BeiDou-3 / GNSS observations, an adaptive factor is proposed to correct the predicted value of the state vector in step S2.

[0010] S4. Obtain vector K and the updated state vector covariance through step S3;

[0011] S5. Considering that there are still gross errors in the BeiDou-3 / GNSS carrier phase observations, a robustness factor M is introduced to determine the weight of each type of observation.

[0012] S6. Use the corrected measurement covariance matrix Update the K matrix and the state covariance matrix;

[0013] S7. Calculate the updated state vector.

[0014] Furthermore, the observation equation for step S1 is:

[0015] , .

[0016] Furthermore, the calculation formula for step S2 is as follows:

[0017]

[0018]

[0019] in, It is a state vector, where - represents the predicted value and + represents the updated value. k and k -1 indicates two adjacent epochs. Represents the transition matrix. The state vector covariance matrix is ​​represented by the following: The process noise represents the covariance matrix.

[0020] Furthermore, the calculation formula for step S3 is as follows:

[0021]

[0022] in and It's experience points. =2, =3.5;

[0023] This is an intermediate calculated value, represented as:

[0024]

[0025] in It is a state vector estimate calculated using the new observations;

[0026] tr represents the trace of the matrix.

[0027] Furthermore, the calculation formula for step S4 is as follows:

[0028]

[0029] .

[0030] Furthermore, the calculation formula for step S5 is as follows:

[0031]

[0032] in express F Test statistic and Significance level and Below F Test value, significance level , ;

[0033] Indicates degrees of freedom;

[0034] Corrected covariance matrix of observations elements

[0035]

[0036] in, and These represent the pseudorange and carrier phase noise values ​​for each satellite, respectively.

[0037] It is obtained by solving the original covariance matrix;

[0038] R is the classification factor for GPS and BeiDou satellites.

[0039] .

[0040] Furthermore, the calculation formula for step S6 is as follows:

[0041]

[0042] .

[0043] Furthermore, the calculation formula for step S7 is as follows:

[0044]

[0045] in This represents a linear combination of observations from BeiDou and GPS.

[0046] Compared with existing technologies, the beneficial effects of this solution are:

[0047] 1. Traditional methods treat the station coordinates as unknowns. After obtaining the station coordinates, the deformation is obtained by subtracting the coordinates. This method suffers from the problem of gradual error accumulation. Its drawback is that the accuracy is only at the centimeter level, with errors accumulating gradually. Furthermore, the traditional method first solves for the monitoring station coordinates based on the BeiDou-3 / GNSS satellite range intersection method, and then obtains the deformation by subtracting the coordinates from the two periods, which is a two-step solution. In contrast, this scheme treats the bridge structural deformation as an unknown parameter and considers the gross errors caused by the influence of errors in the carrier phase observations from the monitoring station to the BeiDou-3 / GNSS satellites, solving for the bridge structural deformation in a single step.

[0048] 2. This scheme uses the deformation value of the bridge structure monitoring station as the error source of the carrier phase observation. It analyzes the influence of the deformation of the bridge structure monitoring station on the carrier phase observation, treats the bridge structure deformation as an unknown parameter, and directly calculates the deformation in one step without error accumulation. Furthermore, considering the gross errors in the BeiDou-3 / GNSS carrier phase observations due to environmental obstruction, such as the ionosphere and troposphere, an adaptive factor robustness solution algorithm is derived. Attached Figure Description

[0049] Figure 1 This is a schematic diagram of traditional bridge deformation monitoring based on North-South technology in the background technology;

[0050] Figure 2 This is a schematic diagram illustrating the change in carrier phase observation caused by station deformation in this embodiment;

[0051] Figure 3 This is the deformation monitoring point for the cross-water bridge retrieved by BeiDou-3 / GNSS in this embodiment;

[0052] Figure 4 This is a comparison chart of the deformation variables calculated by the solution method used in this embodiment and the traditional method;

[0053] Figure 5 This is a comparison chart of the error between the solution method used in this embodiment and the traditional method. Detailed Implementation

[0054] The present invention will be further described in detail below through specific embodiments:

[0055] Example

[0056] The deformation of the bridge monitoring station causes changes in the distance between the station and the satellite, significantly impacting the high-precision data processing of the BeiDou-3 system. A schematic diagram illustrating the changes in carrier phase observations caused by station deformation is shown below. Figure 2 As shown.

[0057] exist Figure 2 middle, This refers to satellites observed at the same time. The station coordinates do not consider bridge deformation. It is the distance between the satellite and the station R. The coordinates of the measuring station take into account the bridge deformation. Satellites and stations The distance between them. It is the origin of the station's coordinate system. These are satellite coordinates, and station coordinates that take into account bridge deformation. . This takes into account the coordinate displacement of the measuring station caused by bridge deformation. These represent the components in the north, east, and vertical directions, respectively. This is an estimate that takes into account the clock bias of the bridge deformation receiver. This is an estimate that does not take into account the clock bias of the receiver due to bridge deformation. The distance is a very small amount compared to the orbital altitude of a satellite exceeding 20,000 km, therefore calculating the satellite's elevation angle is extremely difficult. and azimuth Changes in station coordinates caused by bridge deformation It can be ignored.

[0058]

[0059]

[0060] The change in distance between the satellite and the station caused by bridge deformation is expressed as follows:

[0061]

[0062] in , , The error is caused by the deformation of the bridge, which affects the receiver clock.

[0063] In Precise Point Positioning (PPP) for bridge deformation calculation, traditional data processing treats the station coordinates as unknowns. After calculating the station coordinates, the deformation is obtained through difference, which leads to error propagation and accumulation problems. The station deformation values... For unknown parameters, the solution model is shown in the formula below. The deformation value can be obtained directly in one step.

[0064]

[0065]

[0066] in These are pseudorange observations. These are carrier phase observations. It is the signal frequency. It is the geometric distance between the satellite and the station. It is the bridge deformation value. It is the receiver clock error. It is a tropospheric delay error. It's the wavelength. It is a combined phase ambiguity value. This indicates that all other errors, including those related to Earth's rotation, solid tides, relativity, and antenna phase center correction, are corrected by the corresponding model.

[0067] like Figure 3 As shown, the method for solving the deformation of a cross-water bridge based on BeiDou-3 / GNSS inversion includes the following steps:

[0068] S1. Assuming that station r can observe m satellites at a certain epoch, then establish the observation equation for the carrier phase observations from the BeiDou-3 / GNSS monitoring station to the satellites by combining all satellites. When constructing the observation equation, the bridge deformation is considered as an error source for the carrier phase observations from the bridge structure monitoring station to the satellites, and is listed as an unknown parameter. The observation equation is expressed as follows:

[0069] , .

[0070] S2. Solve the observation equations using the matrix method to obtain the predicted vector of the bridge structural deformation and the covariance matrix of the state vector considering different satellite observation accuracies; the calculation formulas are as follows:

[0071]

[0072]

[0073] in, It is a state vector, where - represents the predicted value and + represents the updated value. k and k -1 indicates two adjacent epochs. Represents the transition matrix. The state vector covariance matrix is ​​represented by the following: The process noise represents the covariance matrix.

[0074] S3. Considering the impact of gross errors in BeiDou-3 / GNSS observations, an adaptive factor is proposed to correct the predicted value of the state vector in step S2; the calculation formula is as follows:

[0075]

[0076] in and It's experience points. =2, =3.5;

[0077] This is an intermediate calculated value, represented as:

[0078]

[0079] in It is a state vector estimate calculated using the new observations;

[0080] tr represents the trace of the matrix.

[0081] S4. Obtain vector K and the updated state vector covariance through step S3; the calculation formula is as follows:

[0082]

[0083] .

[0084] S5. Considering the gross errors in the BeiDou-3 / GNSS carrier phase observations, a robustness factor M is introduced to determine the weight of each type of observation; the calculation formula is as follows:

[0085]

[0086] in express F Test statistic and Significance level and Below F Test value, significance level , ;

[0087] Indicates degrees of freedom;

[0088] Corrected covariance matrix of observations elements

[0089]

[0090] in, and These represent the pseudorange and carrier phase noise values ​​for each satellite, respectively.

[0091] It is obtained by solving the original covariance matrix;

[0092] R is the classification factor for GPS and BeiDou satellites.

[0093] .

[0094] S6. Use the corrected measurement covariance matrix Update the K matrix and the state covariance matrix; the calculation formula is as follows:

[0095]

[0096] .

[0097] S7. The updated state vector is calculated using the following formula:

[0098]

[0099] in This represents a linear combination of observations from BeiDou and GPS.

[0100] Case Comparison:

[0101] like Figure 4 As shown, the data used is from measurements taken on August 12, 2024, at a cross-water bridge in Chongqing between 8:00 AM and 2:00 PM Beijing time. Figure 4 The midpoint represents the deformation of the traditional two-step solution, and the line represents the deformation calculated by the method used in this embodiment.

[0102] like Figure 5 As shown, the traditional method is based on the geometric distance resection method from BeiDou / GNSS satellites to the bridge structure monitoring station, and uses the least squares method to calculate the coordinates of the bridge structure monitoring station. The bridge structure deformation is then obtained through two-stage coordinate difference. The method in this embodiment treats the bridge structure deformation as an unknown parameter in the precise single-point positioning model. Taking gross errors into account, the unknown deformation is directly solved, eliminating errors such as spatial coordinate reference transformation.

[0103] Using the measurement value from the measuring robot as the true value, the root mean square error of the traditional two-step solution is calculated to be 1.9 cm, while the root mean square error of the method described in this embodiment is 0.8 cm, achieving a breakthrough from centimeter-level deformation accuracy to millimeter-level deformation accuracy of the traditional method.

[0104] The above are merely embodiments of the present invention, and common knowledge such as specific structures and / or characteristics in the solutions are not described in detail here. It should be noted that those skilled in the art can make various modifications and improvements without departing from the structure of the present invention, and these should also be considered within the scope of protection of the present invention. These modifications and improvements will not affect the effectiveness of the implementation of the present invention or the practicality of the patent. The scope of protection claimed in this application should be determined by the content of its claims, and the specific embodiments described in the specification can be used to interpret the content of the claims.

Claims

1. A method for solving deformation of a bridge across a water area based on Beidou-3 / GNSS inversion, characterized in that: Includes the following steps: S1. Based on the satellites that can be observed by the bridge structure monitoring station, establish the observation equation from the Beidou-3 / GNSS monitoring station to the satellite carrier phase observation value by combining all satellites; S2. Solve the observation equations using the matrix method to obtain the predicted state vector of the bridge structure deformation and the covariance matrix of the state vector considering different satellite observation accuracies. S3. Considering the impact of gross errors in BeiDou-3 / GNSS observations, an adaptive factor is proposed to correct the predicted value of the state vector in step S2. S4. Obtain vector K and the updated state vector covariance through step S3; S5. Considering that there are still gross errors in the BeiDou-3 / GNSS carrier phase observations, a robustness factor M is introduced to determine the weight of each type of observation. S6, using the revised measurement covariance matrix updating the K matrix and the state covariance matrix S7. Calculate the updated state vector; The calculation formula for step S3 is as follows: ； wherein and is an empirical value, = 2, = 3.5; is an intermediate calculation value, expressed as: ； wherein is the predicted value of the epoch k state vector, is the state vector estimate computed using the new observation. tr represents the trace of the matrix; The calculation formula for step S5 is as follows: ； in express F Test statistic and Significance level and Below F Test value, significance level , ; Indicates degrees of freedom; Corrected covariance matrix of observations elements ； in, and These represent the pseudorange and carrier phase noise values ​​for each satellite, respectively. It is obtained by solving the original covariance matrix; R is the classification factor for GPS and BeiDou satellites. 。 2. The method for solving the deformation of a cross-water bridge based on BeiDou-3 / GNSS inversion according to claim 1, characterized in that: The observation equation for step S1 is: ， 。 3. The method for solving the deformation of a cross-water bridge based on BeiDou-3 / GNSS inversion according to claim 2, characterized in that: The calculation formula for step S2 is as follows: ； ； in, It is the predicted value of the state vector in epoch k. This represents the transition matrix from epoch k-1 to epoch k. This represents the update value of the state vector in epoch k-1. This represents the predicted value of the covariance matrix of the state vector at epoch k. This represents the updated value of the covariance matrix of the state vector at epoch k-1. This represents the matrix transpose of the transition matrix from epoch k-1 to epoch k. The covariance matrix represents the process noise from epoch k-1 to epoch k.

4. The method for solving the deformation of a cross-water bridge based on BeiDou-3 / GNSS inversion according to claim 1, characterized in that: The calculation formula for step S4 is as follows: ； 。 5. The method for solving the deformation of a cross-water bridge based on BeiDou-3 / GNSS inversion according to claim 1, characterized in that: The calculation formula for step S6 is as follows: ； 。 6. The method for solving the deformation of a cross-water bridge based on BeiDou-3 / GNSS inversion according to claim 5, characterized in that: The calculation formula for step S7 is as follows: ； in This represents a linear combination of observations from BeiDou and GPS.

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